6 Discussion
From above analysis, it can be seen that loading path has slight effect on the failure modes under uniaxial compression, the specimen failed with axial splitting. However, the failure modes under triaxial cyclic loading are more complicated than that under triaxial monotonic loading. To explain this phenomenon, the cracks formed in the previous cyclic loading are regarded as the per-existing crack, and the cracks formed in this cyclic loading are regarded as new initiated crack. Figure 12 illustrates crack propagation sketch diagram of specimen containing a single fissure under triaxial compression, bold line and filament represent pre-existing and new cracks, respectively. Under uniaxial, loading tend to initiate vertical crack, thus the crack formed in previous cyclic loading is regarded as the vertical pre-existing fissure, as shown in Fig. 12a. And, the new crack initiate in the tip of fissure, then propagate in the original direction. Therefore, loading path has slight effect on the failure modes under uniaxial compression. Under triaxial compression, loading tend to induce inclined crack, thus the crack formed in pervious cyclic loading is regarded as inclined pre-existing fissure, as shown in Figs. 12b-c. And, the new crack initiate in the tip of fissure, then propagate in various type. Therefore, the failure modes under triaxial cyclic loading are more complicated than that under triaxial monotonic loading. As the failure modes are more complicated under cyclic loading-unloading compression, the shear plane is rougher, which make the residual strength higher than that under monotonic loading, as shown in Fig. 1.
To verify the above assumption, Grain Based Model (GBM) in PFC2D was used to simulate the triaxial cyclic loading-unloading compression of granite after thermal treatment. To generate the GBM that has a microstructure comparable to the rock specimen, the mineralogical composition should keep with the granite in this test, as shown in Table 1. As shown in Fig. 13a, after assigning particles and contact properties according to the minerals, the inter-granular parallel bonds were replaced by Smooth joint (SJ). In general, the micro-parameters used in PFC2D have no direct relationship with the macro-properties in the rock specimen. Calibration has to be strategically carried out using a trial-and-error approach in PFC2D. In the GBM of granite specimen, four different minerals are considered, and corresponding parallel bonds and disks should be assigned with different micro-parameters. Even though the micro-parameters of four minerals cannot quantitatively reflect the mechanism of the grains, these parameters are assigned values in proportion to the real mineral properties suggested by Bass (1995). The micro-parameters for the numerical model of this granite are calibrated using the approach proposed by Peng et al. (2018). The peak strength obtained by simulation results are shown in Fig. 13b, it can be seen that the experimental results are generally captured by the GBM.
To accurately reflect the thermal behavior of granite containing different minerals, the thermal expansion coefficients assigned to the grains as follows: plagioclase, 8.7×10-6K-1; quartz, 24.3×10-6K-1; Amphibole, 28×10-6K-1; biotite, 3.0×10-6K-1 (Fei, 1995; Wittels, 1951). To minimize thermal shock and the development of stress fractures, the temperature of the granite specimens was assumed to change uniformly and in a sufficiently short time (Zhao, 2016, Tian et al., 2018), the temperature of the granite specimen uniformly changed by 1°C every step and then cycle 100 steps. The radius expansion with 1.0046 (Carpenter et al. 1998) is applied to the quartz grains when the temperature elevated to 573°C, and the quartz particle radius shrinks with 0.9954 when the temperature decreases to 573°C. This process can be used to simulate the phase transition of quartz. After thermal treatment, more intra-granular and inter-granular cracks were observed, the inter-granular net around each granite crystal grain was formed and made the ploy grains be isolated with each other (Zhao et al., 2008), and intra-granular crack is dominantly located in the quartz grains, as shown in Fig. 13a. The loading and unloading process simulated by GBM is similar to that in experiment, loading controlled by axial displacement and unloaded controlled by axial stress, as shown in Fig. 13a.
Figure 14 illustrates the comparison of crack propagation characteristic between cyclic and monotonic loading of granite specimens under room temperature and 40 MPa confinement. In Fig. 14c, the serial number represents cycle number, and the serial number in Fig. 14d under monotonic loading correspond with that in Fig. 14c. From Fig. 1d and Fig. 14a, it can be seen that the stress-strain curves of granite under cyclic loading is in good agreement with that under monotonic loading before the peak strength, which means that cyclic loading has slight effect on the crack evolution of granite, and the evolution of micro-crack with axial strain agree well with each other. Due to higher confining pressure, more intra-granular cracks are observed than inter-granular cracks. Micro-cracks dispersed distribute in the specimen, and is mainly parallel to the loading direction. When loading to the peak strength, micro-cracks began to coalesce with each other, and these is also mainly parallel to the loading direction, whereas the direction of micro-cracks under cyclic loading is more complicit than that under monotonic loading. This phenomenon is accordant with that observed by experiment in this paper and that observed by Yang et al. (2015) through micro-CT, and it also verify the above assumption.
After the peak strength, the stress-strain and micro-cracks evolution curves of granite under cyclic loading deviated from these under monotonic loading. The micro-cracks began to increase under unloading process, and it also increases before the stress reach to the previous maximum stress (Felicity effect, Meng et al., 2018). At the moment, the inter-granular and intra-granular cracks of granite under cyclic loading are more than that under monotonic loading, especially for the intra-granular cracks. The macro-cracks have been formed in the specimen under cyclic loading, and the direction is more complicated. However, there is no macro-crack in the specimen under monotonic loading, and the micro-crack is mainly parallel to the loading direction. When the macro-crack has been formed, micro-cracks continuously increase under loading and unloading process, due to friction between macro-cracks. However, increasing rate of micro-crack decreases obviously. When the specimen failed, the failure model of specimen under cyclic loading is more complicated than that under monotonic loading. As the failure modes are more complicated under cyclic loading-unloading compression, the shear plane is rougher, which lead to the residual strength is higher than that under monotonic loading.
More thermal micro-cracks were induced in the specimen when T = 600°C, and the crack evolution characteristic of specimen under cyclic loading is different from that under monotonic loading, as shown in Fig. 15a, which is accordant well with that obtained by experiment, as shown in Fig. 1c. Due to the bearing structure destroyed by high temperature, micro-crack continuously increases under unloading and loading process. Therefore, the stress-strain and micro-crack evolution curves separated with each other under cyclic and monotonic loading after the first loading. When the specimen was loaded by 5 cycles, the inter-granular cracks of specimen under cyclic loading are more than that under monotonic loading, whereas the intra-granular cracks near equal with each other. It indicates that inter-granular are easier to propagate than intra-granular under loading and unloading process. Due to more micro-cracks were induced under cyclic loading, the peak strength under cyclic loading is lesser than that under monotonic loading. This phenomenon can be also seen in experimental result, as shown in Fig. 1c. The micro-cracks induced by loading is lesser than that induced by thermal treatment, the direction of micro-crack is randomly, and it is slightly effected by cyclic loading process.
After the peak strength, stress decreases gradually, the stress-strain and micro-crack evolution curves under cyclic loading deviated from these under monotonic loading obviously. At this point, micro-cracks coalesced with each other, and no macro-crack formed. When the specimen failed, stress decreases quickly under monotonic loading, and more intra-granular cracks were observed than that under cyclic loading, which means that the quick decrease of stress is easier to induce intra-granular crack. At this moment, the splitting tensile macro-cracks were observed in specimens, which is accordant well with that obtained by experiment, as shown in Fig. 13a.